On the Mordell-Weil rank of an abelian variety over a number field
type: Item
instance of: scholarly article
title: On the Mordell-Weil rank of an abelian variety over a number field
zbMATH Open document ID: 0686.14025
DOI: 10.1016/0022-4049(89)90041-8
author: Takeshi Ooe
author: Jaap Top
published in: Journal of Pure and Applied Algebra
publication date: 1989-01-01T00:00:00Z
review text: The authors give a bound for the rank of the Mordell-Weil group of an abelian variety A over a number-field K. The bound depends only on the dimension, the degree [K:\({\mathbb{Q}}]\) and the conductor of A. The proof uses the injection \(A(K)/2\cdot A(k)\subseteq H^ 1(K,A[2])\), and a bound on the order of the cohomology obtained by estimating discriminants.
Mathematics Subject Classification ID: 14G25
Mathematics Subject Classification ID: 14K05
Mathematics Subject Classification ID: 14G05
zbMATH DE Number: 4123881
zbMATH Keywords: bound for the rank of the Mordell-Weil group
MaRDI profile type: Publication
full work available at URL: 0022-4049(89)90041-8
OpenAlex ID: W2170877689
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reviewed by: Gerd Faltings
description: scientific article; zbMATH DE number 4123881